A polycrystalline Ni41Co9Mn40Sn10 (at. %) magnetic shape memory alloy was prepared by arc melting and characterized mainly by magnetic measurements, in-situ high-energy X-ray diffraction (HEXRD), and mechanical testing. A large magnetoresistance of 53.8% (under 5 T) and a large magnetic entropy change of 31.9 J/(kg K) (under 5 T) were simultaneously achieved. Both of these values are among the highest values reported so far in Ni-Mn-Sn-based Heusler alloys. The large magnetic entropy change, closely related to the structural entropy change, is attributed to the large unit cell volume change across martensitic transformation as revealed by our in-situ HEXRD experiment. Furthermore, good compressive properties were also obtained. Lastly, the combination of large magnetoresistance, large magnetic entropy change, and good compressive properties, as well as low cost makes this alloy a promising candidate for multifunctional applications.